Uniformly Strong Persistence for a Delayed Predator-Prey Model

An asymptotically periodic predator-prey model with time delay is investigated. Some sufficient conditions for the uniformly strong persistence of the system are obtained. Our result is an important complementarity to the earlier results

Persistence and Global Dynamics of an Extended Rosenzweig-MacArthur Model

This paper investigates persistence and global dynamics of a tritrophic food chain model consisting of prey, predator, and super-predator. We establish dissipativeness, ultimate boundedness of an invariant region in the state space of this model via the notion of omega-limit sets, absorbing region and global attractor. We explore Freedman-Waltman theorem, and Bendixson-Dulac theorem to guarantee persistence conditions of the model. Lyapunov’s functionals and Lyapunov-LaSalle invariance principle ensure the existence of global asymptotic stability of the system. Numerical responses, phase-portrait and phase-flows were used to illustrate propositions and lemmas. Key words: Global asymptotic stability; Lyapunov functional; Persistence